VHA REcruitment, HIring, and REtention Act of 2017 or VHA REHIRE Act of 2017 This bill authorizes the Department of Veterans Affairs (VA) to carry out a VA Student Loan Repayment Program to assist the Veterans Health Administration (VHA) meet staffing needs for health professional occupations for which recruitment or retention of qualified personnel is difficult. A program participant must agree to serve as a full-time VHA employee for one year for every $10,000 of received benefits, with a minimum three-year commitment. Program assistance may be in addition to assistance available under the VA Educational Assistance Program. A participant in the VA Education Debt Reduction Program must agree to serve as a full-time VHA employee for at least three years. A physician, dentist, podiatrist, chiropractor, optometrist, registered nurse, physician assistant, or dental auxiliary must agree to serve at least two years as a full-time VA employee in order to receive certain bonuses or allowances. The VA shall offer employment to a qualified VHA applicant within 75 days after the last day applications are accepted for a position.